This invention generally relates to the manufacture of paperboard products. In particular, the invention relates to methods and apparatus for predicting score-line cracking propensity in paperboard products having multiple plies.
There have been available few tests for evaluating score-line cracking, for instance, the score cracking angle test disclosed by Whitsitt and McKee in xe2x80x9cInvestigation of Improved Device for Evaluating the Cracking Potential of Linerboard,xe2x80x9d Institute of Paper Chemistry Summary Report, Project No. 1108-29 (1996). This test, first developed at the Institute of Paper Chemistry, fails to either measure a fundamental material property, or detect damage in a single ply. No meaningful correlations have thus been found over the years to score-line cracking performance in the field.
A recent test, disclosed by J. Gonzalez in xe2x80x9cScore Cracking in Linerboard,xe2x80x9d M. S. Dissertation (No. 6190-Research), Institute of Paper Science and Technology, Georgia (2000), is not so much a predictive test, but rather is a set-up that attempts to replicate, rather poorly, scoring. It does not scientifically measure any board property that may prove to correlate to score-line cracking propensity in the field. The test comprises two motor-driven horizontal metal wheels forming essentially a nip compression. A linerboard sample (25 cmxc3x9712 cm), manually folded in half and fed between the flat metal wheels, undergoes a nip-type compressive force. The cracking percent of the folded sample is then measured visually or using a microscope.
Experimental work carried out at International Paper""s Corporate Research Center in the period February-May, 2000 has been instrumental in providing insight into the root causes of the propensity for score-line cracking in white-top linerboard (especially 69 lb.). The mechanistic basis for designing a score-line-crack-resistant two-ply linerboard is grounded in three (non-mutually exclusive) functional factors: (1) the ability of the top ply to undergo large plastic (irreversible) deformation prior to failure; (2) the ability of the base ply to compress elastically while the top ply is deforming (plastically); and (3) in order for (1) and (2) to simultaneously apply, the interlaminar (ply) bond must be low enough (but adequate to ensure against delamination) to allow the top ply to xe2x80x9cslidexe2x80x9d over the base ply. Achieving this requires the development of a testing method capable of predicting plastic deformations, or the fracture toughness, of the top ply alone, and able to correlate such a measurement with score-line cracking propensity in the field.
In materials science and engineering, the term xe2x80x9cmaterialxe2x80x9d has a precise meaning. It refers to either a pure substance or an alloy that can be approximated as essentially homogeneous in composition. When more than one substance or material are combined, and when this combination has internal structural heterogeneity, the term xe2x80x9ccomposite materialxe2x80x9d is used. According to this definition, wood fibers may be regarded as composite materials, or, specifically, composite tubes of cellulosic microfibrils embedded in an amorphous matrix of hemicellulose and lignin. Structurally, paper or board is, however, a network. On a microscopic scale, paper or board is a cellulosic network of crossing fibers filled with voids; macroscopically, it could be regarded as a continuum with inherent (micro)cracks and flaws being xe2x80x9csmeared outxe2x80x9d for the purpose of simplifying analysis. For practical issues related, for instance, to box construction, such as scoring, it may be deemed appropriate that linerboard be dealt with as a continuum whose material properties and structural analysis are determined relying on theories of elasticity and plasticity from the field of solid mechanics. Thus, two-ply linerboard constructs comprise two elastic-plastic sheet-like materials whose properties may be analyzed orthotropically. Safeguarding against, for instance, cracking in the top ply during scoring would necessitate attention principally to: i) the extent of (plastic) deformability in each ply; and ii) inter-ply stresses.
Linear elastic materials load and unload along the same path (see FIG. 1); crack growth in such a material can be represented graphically by the load-displacement curve depicted in FIG. 2. The curve is linear up to the point of crack propagation, and the displacement is zero when the specimen is unloaded. The energy consumed in the fracture process is therefore equivalent to the area enclosed under the curve. The irreversible work consumed during elastic fracture is confined to thin boundary layers along the faces of the propagating crack.
Paper and board, however, are tough, ductile materials (the extent of which depends on furnish composition and papermaking conditions) whose yield stress is low (see FIG. 3). When such a material is strained, it yields not only at the point(s) of crack initiation, but away from these points too. Thus, irreversible deformation is no longer confined to the thin boundary layer along the faces of the propagated crack (as in elastic fracture), but is spread throughout the material. In addition to the work required in the crack tip process zone, significant irreversible work is consumed in the yielded regions away from the crack. It is important to recognize that the plastic deformation outside the fracture process zone is not essential to the process of fracture. Consequences of the plastic flow include curvature in the load-displacement curve on loading, and displacement irreversibilities upon unloading, both in a specimen without a crack (FIG. 3) and a specimen with a crack (FIG. 4).
The work done during loading, given by the area under the load-displacement curve in FIG. 4, represents the combined contribution to fracture and remote flow. These two works are difficult to separate experimentally. However, a methodology is needed to separate the elastic and plastic portions of the fracture energy consumed in deforming the top-ply of two-ply linerboard systems. This methodology should be designed so that the measured plastic contribution of the work done during the fracture process correlates well with predicting the propensity of linerboard to score-line cracking during converting operations.
The present invention is directed to a method and an apparatus for predicting a score-line cracking propensity of a multi-ply substrate. The method comprises the steps of: bending the multi-ply substrate; acquiring data from the multi-ply substrate during bending; and computing a material property of a top ply of the multi-ply substrate based on the acquired data. The material property must show a strong correlation to the score-line cracking propensity of the multi-ply substrate. In accordance with the preferred embodiment of the invention, the material property which is computed is the energy consumed in plastic deformation of the top ply during the fracture process. The measurement results can be used to predict score-line cracking propensity in multi-ply board systems. In accordance with the preferred embodiment, the substrate is paperboard.
Also in accordance with the preferred embodiment, the apparatus is implemented as a top-ply fracture tester designed to bend a sample of a multi-ply substrate and acquire data during bending from which the plastic energy consumption during the fracture process can be automatically computed. The tester comprises two clamps in which the sample is placed; one of the clamps is fixed, the other rotates the sample around a spindle. When bending the sample, it is under a net tensile force, which is recorded using a load cell. A computer receives inputs from the load cell and from a position detector which detects the position of the rotating clamp during the sample bending operation. The computer is programmed to compute the energy consumed during plastic deformation of the top ply of the multi-ply substrate. This top-ply fracture tester induces fracture in the top ply only, and allows the identification of elastic and plastic regions in a single ply. Score-line cracking resistance essentially emanates from the ability of the sheet to deform plastically (in the top ply).
The test and analysis methods in accordance with the preferred embodiment characterize failure in the outermost ply of a multi-ply linerboard system. The test method specifically measures cracking resistance, and correlates board functionality to field performance (converting operations), by accurately measuring the nonlinear, plastic deformation of the ply, or plastic fracture energy.
In accordance with the teaching of the invention, material changes in the board can be correlated with xe2x80x9cdamagexe2x80x9d phenomena, occurring physically, which are relatively easily detectable. When a two-ply linerboard sample is tested as described above, an operator would visually notice three distinct phenomena taking place at three discrete intervals: (1) the development of a (macro)crack as the sample is bent around the spindle; (2) the opening up of the (macro)crack; and (3) the complete separation of the fibers, just prior to eventual failure and delamination of the top ply from the base ply. These stages are respectively referred to herein by the terms xe2x80x9ccrack,xe2x80x9d xe2x80x9cgapxe2x80x9d and xe2x80x9cflap.xe2x80x9d These stages represent the entire zone of plastic deformation while subjecting the top ply to a net tensile state of stress. Plastic deformation in linerboard is thus characterized by two components: the energy consumed during the transition from crack to gap and that consumed during the transition from gap to flap. Each component, or both, may be optimized to improve certain aspects of the board""s ability to deform plastically, and, in turn, resistance to cracking.
In accordance with the preferred method, the operator records the visual detection of the crack, gap and flap by pressing a pre-specified alphanumeric key (on the computer keypad) for each event. The computer is programmed to detect these specific key depressions. Once the test is complete, the computer program computes the (elastic and plastic) energies consumed from inception to failure of the single ply. Generally, the following is determined from a specimen""s load-elongation curve: (1) energy consumed during elastic deformation (up to crack initiation); (2) energy consumed during the crack-to-gap transition (the first plastic component); (3) energy consumed during the gap-to-flap transition (second plastic component); and (4) energy consumed during the crack-to-flap transition (total plastic contribution, or sum of energy components (2) and (3)). The computer is also preferably programmed to compute the standard deviations, which may further help indicate two things: operator""s precision (the larger the standard deviation, the worse is the operator""s accuracy for identifying crack, gap and flap) and sample variability (for instance, the standard deviation tends to be higher for recycle furnishes owing to inherent variability in pulp quality and, hence, mechanical properties of the board).
Thus the top-ply fracture tester disclosed herein enables one to instantaneously obtain a load-displacement curve for each ply of a multi-ply linerboard system, or any similar multi-ply structure. From the individual load-elongation curve, each ply""s elastic and plastic components are computed and analyzed. For white-top linerboard, it is shown that the top ply is characterized by a two-component plastic zone of deformation, which are respectively referred to herein as the xe2x80x9ccrack-to-gapxe2x80x9d and the xe2x80x9cgap-to-flapxe2x80x9d components. An unequivocal correlation has been shown between the energy consumed during the crack-to-flap transition (the whole plastic zone) and the propensity for score-line cracking in the field. The plastic zone characterization also serves as a litmus test, which would be useful for proposing ways to improve the board""s mechanical performance under varying papermaking conditions, furnish type and board structural configuration.